Large oscillations of the argument of Rankin–Selberg L-functions

In this paper, we study the argument of Rankin–Selberg L -functions associated to holomorphic cusp forms in both weight aspect and t -aspect. Let S ( t , f × f ) : = 1 π ℑ log L 1 2 + i t , f × f . Assuming the generalized Riemann hypothesis (GRH), we prove that S ( t , f × f ) = Ω ± ( log k t log log log k t log log k t ) , where k is the weight of the form f .